Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 + 14}{x - 7} = \dfrac{12x - 21}{x - 7}$
Answer: Multiply both sides by $x - 7$ $ \dfrac{x^2 + 14}{x - 7} (x - 7) = \dfrac{12x - 21}{x - 7} (x - 7)$ $ x^2 + 14 = 12x - 21$ Subtract $12x - 21$ from both sides: $ x^2 + 14 - (12x - 21) = 12x - 21 - (12x - 21)$ $ x^2 + 14 - 12x + 21 = 0$ $ x^2 + 35 - 12x = 0$ Factor the expression: $ (x - 5)(x - 7) = 0$ Therefore $x = 5$ or $x = 7$ However, the original expression is undefined when $x = 7$. Therefore, the only solution is $x = 5$.